import numpy as np
from scipy import linalg


def calculate_frechet_distance(mu1, sigma1, mu2, sigma2, eps=1e-6):
    mu1 = np.atleast_1d(mu1)
    mu2 = np.atleast_1d(mu2)

    sigma1 = np.atleast_2d(sigma1)
    sigma2 = np.atleast_2d(sigma2)

    assert mu1.shape == mu2.shape, 'Training and test mean vectors have different lengths'
    assert sigma1.shape == sigma2.shape, 'Training and test covariances have different dimensions'

    diff = mu1 - mu2

    # Product might be almost singular
    covmean, _ = linalg.sqrtm(sigma1.dot(sigma2), disp=False)
    if not np.isfinite(covmean).all():
        print('fid calculation produces singular product; adding %s to diagonal of cov estimates' % eps)
        offset = np.eye(sigma1.shape[0]) * eps
        covmean = linalg.sqrtm((sigma1 + offset).dot(sigma2 + offset))

    # Numerical error might give slight imaginary component
    if np.iscomplexobj(covmean):
        if not np.allclose(np.diagonal(covmean).imag, 0, atol=1e-3):
            m = np.max(np.abs(covmean.imag))
            raise ValueError('Imaginary component {}'.format(m))
        covmean = covmean.real

    return diff.dot(diff) + np.trace(sigma1) + np.trace(sigma2) - 2 * np.trace(covmean)


def calculate_fid_given_features(feature1, feature2):
    mu1 = np.mean(feature1, axis=0)
    sigma1 = np.cov(feature1, rowvar=False)
    mu2 = np.mean(feature2, axis=0)
    sigma2 = np.cov(feature2, rowvar=False)
    fid_value = calculate_frechet_distance(mu1, sigma1, mu2, sigma2)

    return fid_value